Using rational approximations, what is an inequality statement comparing 21−−√

Question

and 17−−√
? Enter <, >, or =

Answer 1

To compare \( \sqrt{21} \) and \( \sqrt{17} \) using rational approximations, we can calculate the square roots or use known rational approximations for better accuracy.

1. Calculate the approximate values of the square roots:

   • \( \sqrt{21} \approx 4.583 \)
   • \( \sqrt{17} \approx 4.123 \)

2. Comparison:

   Since \( 4.583 > 4.123 \), we can say:

   \[ \sqrt{21} > \sqrt{17} \]

Thus, the inequality statement is:

\[ \sqrt{21} > \sqrt{17} \]